Microservices based architectures are increasingly widespread in the cloud software industry. Still, there is a shortage of auto-scaling methods designed to leverage the unique features of these architectures, such as the ability to independently scale a subset of microservices, as well as the ease of monitoring their state and reciprocal calls. We propose to address this shortage with ATOM, a model-driven autoscaling controller for microservices. ATOM instantiates and solves at run-time a layered queueing network model of the application. Computational optimization is used to dynamically control the number of replicas for each microservice and its associated container CPU share, overall achieving a fine-grained control of the application capacity at run-time. Experimental results indicate that for heavy workloads ATOM offers around 30%-37% higher throughput than baseline model-agnostic controllers based on simple static rules. We also find that model-driven reasoning reduces the number of actions needed to scale the system as it reduces the number of bottleneck shifts that we observe with model-agnostic controllers.